This question concerns bit strings of length six. These bit strings can be divided up into four types depending on their

initial and terminal bit. Thus the types are: $0$XXXX$0,0$XXXX$1,1$XXXX$0,1$XXXX$1.$

How many bit strings of length six must you select before you are sure to have at least $4$ that are of the same type?

$($Assume that when you select bit strings you always select different ones from ones you have already selected.$)$